James A. Sellers

activity

20242026

collaborators

7 papers

math.NT2026

Elementary proofs of congruences modulo 5 for overpartitions with restricted odd differences

Bishnu Paudel, James A. Sellers, Haiyang Wang

In 2015, Bringmann, Dousse, Lovejoy, and Mahlburg defined the function $t (n)$ to be the number of overpartitions of weight $n$ where (i) the difference between two succe…

math.NT2026

Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction

Bishnu Paudel, James A. Sellers, Haiyang Wang

In 2021, Chern and Tang introduced two families of two-parameter modular functions associated with the Rogers-Ramanujan continued fraction. They established recurrence relations th…

math.NT2025

Elementary Proofs of Recent Congruences for Overpartitions Wherein Non-Overlined Parts are Not Divisible by 6

Bishnu Paudel, James A. Sellers, Haiyang Wang

We define $R_{l}^{*} (n)$ as the number of overpartitions of $n$ in which non-overlined parts are not divisible by $l$ . In a recent work, Nath, Saikia, and the second author…

math.CO2025

Overpartitions and Kaur, Rana, and Eyyunni's mex sequences

Brian Hopkins, James A. Sellers

Kaur, Rana, and Eyyunni recently defined the mex sequence of a partition and established, by analytic methods, connections to two disparate types of partition-related objects. We m…

math.NT2025

Extending Recent Congruence Results on $(ℓ, μ)$ -Regular Overpartitions

Bishnu Paudel, James A. Sellers, Haiyang Wang

Recently, Alanazi, Munagi, and Saikia employed the theory of modular forms to investigate the arithmetic properties of the function $R_{ℓ, μ} (n)$ , which enumerates the…

math.NT2025

Extending recent work of Nath, Saikia, and Sarma on $k$ -tuple $ℓ$ -regular partitions

Bishnu Paudel, James A. Sellers, Haiyang Wang

Let $T_{ℓ, k} (n)$ denote the number of $ℓ$ -regular $k$ -tuple partitions of $n$ . In a recent work, Nath, Saikia, and Sarma derived several families of congruences for $T_{\ell,…

math.CO2024

Enumeration modulo 4 of overpartitions wherein only even parts can be overlined

Aidan Carlson, Brian Hopkins, James A. Sellers

In 2014, as part of a larger study of overpartitions with restrictions of the overlined parts based on residue classes, Munagi and Sellers defined $d_{2} (n)$ as the number of overpar…

Elementary proofs of congruences modulo 5 for overpartitions with restricted odd differences

Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction

Elementary Proofs of Recent Congruences for Overpartitions Wherein Non-Overlined Parts are Not Divisible by 6

Overpartitions and Kaur, Rana, and Eyyunni's mex sequences

Extending Recent Congruence Results on (ℓ,μ)-Regular Overpartitions

Extending recent work of Nath, Saikia, and Sarma on k-tuple ℓ-regular partitions

Enumeration modulo 4 of overpartitions wherein only even parts can be overlined

Extending Recent Congruence Results on $(ℓ, μ)$ -Regular Overpartitions

Extending recent work of Nath, Saikia, and Sarma on $k$ -tuple $ℓ$ -regular partitions